The Impact of Imperfect Timekeeping on Quantum Control

TL;DR

This paper investigates how imperfect timekeeping affects quantum control, showing limitations on circuit complexity and cooling efficiency due to timing errors, using bounds on gate fidelity and thermodynamic processes.

Contribution

It introduces a framework linking imperfect timekeeping to quantum control limitations, deriving bounds on gate fidelity and demonstrating robustness in quantum cooling processes.

Findings

Imperfect timekeeping limits achievable circuit complexity.

Timing errors only affect cooling rate, not the final temperature.

Derived upper bounds on average gate fidelity under timing imperfections.

Abstract

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter which no physical clock can ever perfectly characterise. In this letter, we study how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. We show that the quality of timekeeping an agent has access to limits the circuit complexity they are able to achieve within circuit-based quantum computation. We do this by deriving an upper bound on the average gate fidelity achievable under imperfect timekeeping for a general class of random circuits. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.